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evablogger [386]
3 years ago
14

The diameter of one circle is represented by 12x. The diameter of another circle is represented by 6x^2y. What is the ratio of t

he radii of the two circles?
Mathematics
2 answers:
Luda [366]3 years ago
5 0
12x/2=6x---------
(6x)^2y=6^2y.x^2y-------

Vesnalui [34]3 years ago
4 0
D/2=r
\frac{r_1}{r_2}= \frac{ \frac{d_1}{2} }{ \frac{d_2}{2} }  = \frac{d_1}{d_2}

so we don't even need to convert
12x:6x²y
divide both sides by 6x
2:xy
the ratio is 2:xy
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A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation
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Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an m\times n matrix.  Let T :U\to V  be the corresponding linear transformationover the field F and \theta be identity vector in V. Now if x\in Ker( T)\implies T(x)=\theta.

(1) The kernel of a linear transformation is a vector space : True.

Let x,y\in Ker( T), then,

T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)

hence the kernel is closed under addition.

Let \lambda\in F, x\in Ker( T), then

T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta

\lambda x\in Ker(T) and thus Ket(T) is closed under multiplication

Finally, fore all vectors u\in U,

T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta

\implies \theta\in Ker(T)

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is \mathbb R^m : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in \mathbb R^m

: False

The null space that is dimension of solution space of an m x n matrix is always in \mathbb R^n.

(4) The column space of A is the range of the mapping x\to Ax

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

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Step-by-step explanation:

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alexgriva [62]

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Step-by-step explanation:

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